\newproblem{lay:2_7_3}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 2.7.3}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  Find the $3\times 3$ matrix that translate by $(2,1)$ and then rotate by $90\degree$ about the origin in 2D using homogeneous coordinates.
}{
  % Solution
	The required transformation is
	\begin{center}
		$\tilde{A}=\begin{pmatrix}\cos(90\degree) & \sin(90\degree) & 0 \\ -\sin(90\degree) & \cos(90\degree) & 0  \\ 0 & 0 & 1\end{pmatrix}
		   \begin{pmatrix}1 & 0 & 2\\ 0 & 1 & 1 \\ 0 & 0 & 1\end{pmatrix}
			=\begin{pmatrix}0 & 1 & 1\\ -1 & 0 & -2 \\ 0 & 0 & 1\end{pmatrix}$
	\end{center}
}
\useproblem{lay:2_7_3}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
